Sevilla Francisco J, Valdés-Gómez Adriano, Torres-Carbajal Alexis
Instituto de Física, <a href="https://ror.org/01tmp8f25">Universidad Nacional Autónoma de México</a>, P.O. Box 20-364, 01000 Ciudad de México, Mexico.
AI Factory at BBVA México.
Phys Rev E. 2024 Jul;110(1-1):014113. doi: 10.1103/PhysRevE.110.014113.
A model for anomalous transport of tracer particles diffusing in complex media in two dimensions is proposed. The model takes into account the characteristics of persistent motion that an active bath transfers to the tracer; thus, the model proposed here extends active Brownian motion, for which the stochastic dynamics of the orientation of the propelling force is described by scaled Brownian motion (sBm), identified by time-dependent diffusivity of the form D_{β}∝t^{β-1}, β>0. If β≠1, sBm is highly nonstationary and suitable to describe such nonequilibrium dynamics induced by complex media. In this paper, we provide analytical calculations and computer simulations to show that genuine anomalous diffusion emerges in the long-time regime, with a time scaling of the mean-squared displacement t^{2-β}, while ballistic transport t^{2}, characteristic of persistent motion, is found in the short-time regime. We also analyze the time dependence of the kurtosis, and the intermediate scattering function of the position distribution, as well as the propulsion autocorrelation function, which defines the effective persistence time.
提出了一个二维复杂介质中示踪粒子扩散异常输运的模型。该模型考虑了活性浴传递给示踪粒子的持续运动特性；因此，这里提出的模型扩展了活性布朗运动，对于活性布朗运动，推进力方向的随机动力学由标度布朗运动（sBm）描述，其由形式为(D_{β}∝t^{β - 1})，(β > 0)的时间相关扩散系数确定。如果(β≠1)，sBm是高度非平稳的，适合描述由复杂介质引起的这种非平衡动力学。在本文中，我们提供了解析计算和计算机模拟，以表明在长时间区域出现真正的异常扩散，平均平方位移的时间标度为(t^{2 - β})，而在短时间区域发现了持续运动特征的弹道输运(t^{2})。我们还分析了峰度的时间依赖性、位置分布的中间散射函数以及定义有效持续时间的推进自相关函数。
